Calculus Examples

$\int_{0}^{300} \frac{4}{5} \cdot \sqrt[4]{x^{5}} d x$

Step 1

Since $\frac{4}{5}$ is constant with respect to $x$ , move $\frac{4}{5}$ out of the integral.

$\frac{4}{5} \int_{0}^{300} \sqrt[4]{x^{5}} d x$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{x^{5}}$ as $x^{\frac{5}{4}}$ .

$\frac{4}{5} \int_{0}^{300} x^{\frac{5}{4}} d x$

Step 3

By the Power Rule, the integral of $x^{\frac{5}{4}}$ with respect to $x$ is $\frac{4}{9} x^{\frac{9}{4}}$ .

$\frac{4}{5} \frac{4}{9} x^{\frac{9}{4}}]_{0}^{300}$

Step 4

Substitute and simplify.

Tap for more steps...

Step 4.1

Evaluate $\frac{4}{9} x^{\frac{9}{4}}$ at $300$ and at $0$ .

$\frac{4}{5} ((\frac{4}{9} \cdot 300^{\frac{9}{4}}) - \frac{4}{9} \cdot 0^{\frac{9}{4}})$

Step 4.2

Simplify.

Tap for more steps...

Step 4.2.1

Combine $\frac{4}{9}$ and $300^{\frac{9}{4}}$ .

$\frac{4}{5} (\frac{4 \cdot 300^{\frac{9}{4}}}{9} - \frac{4}{9} \cdot 0^{\frac{9}{4}})$

Step 4.2.2

Rewrite $0$ as $0^{4}$ .

$\frac{4}{5} (\frac{4 \cdot 300^{\frac{9}{4}}}{9} - \frac{4}{9} \cdot {(0^{4})}^{\frac{9}{4}})$

Step 4.2.3

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{4}{5} (\frac{4 \cdot 300^{\frac{9}{4}}}{9} - \frac{4}{9} \cdot 0^{4 (\frac{9}{4})})$

Step 4.2.4

Cancel the common factor of $4$ .

Tap for more steps...

Step 4.2.4.1

Cancel the common factor.

$\frac{4}{5} (\frac{4 \cdot 300^{\frac{9}{4}}}{9} - \frac{4}{9} \cdot 0^{4 (\frac{9}{4})})$

Step 4.2.4.2

Rewrite the expression.

$\frac{4}{5} (\frac{4 \cdot 300^{\frac{9}{4}}}{9} - \frac{4}{9} \cdot 0^{9})$

Step 4.2.5

Raising $0$ to any positive power yields $0$ .

$\frac{4}{5} (\frac{4 \cdot 300^{\frac{9}{4}}}{9} - \frac{4}{9} \cdot 0)$

Step 4.2.6

Multiply $0$ by $- 1$ .

$\frac{4}{5} (\frac{4 \cdot 300^{\frac{9}{4}}}{9} + 0 (\frac{4}{9}))$

Step 4.2.7

Multiply $0$ by $\frac{4}{9}$ .

$\frac{4}{5} (\frac{4 \cdot 300^{\frac{9}{4}}}{9} + 0)$

Step 4.2.8

Add $\frac{4 \cdot 300^{\frac{9}{4}}}{9}$ and $0$ .

$\frac{4}{5} \cdot \frac{4 \cdot 300^{\frac{9}{4}}}{9}$

Step 4.2.9

Multiply $\frac{4}{5}$ by $\frac{4 \cdot 300^{\frac{9}{4}}}{9}$ .

$\frac{4 (4 \cdot 300^{\frac{9}{4}})}{5 \cdot 9}$

Step 4.2.10

Multiply $4$ by $4$ .

$\frac{16 \cdot 300^{\frac{9}{4}}}{5 \cdot 9}$

Step 4.2.11

Multiply $5$ by $9$ .

$\frac{16 \cdot 300^{\frac{9}{4}}}{45}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{16 \cdot 300^{\frac{9}{4}}}{45}$

Decimal Form:

$133177.32640921$

Step 6